I'm trying to determine whether or not an anti-alias filter is needed for sampling square waves. The goal is to sample square wave pulses from a video detector with an ADC, do some time-domain digital processing on it, and reconstruct it with a DAC.
I do understand that signals with frequencies above the nyquist rate will alias into the "wrong" frequency bin. I guess the best analogy is the camera taking a picture of a car wheel turning at a certain rate, and at certain speeds it looks like the wheel stops or starts spinning backwards (a "misinterpretation" caused by the aliased frequencies). A square wave is made up of an infinite amount of odd harmonics but....
From an ADC perspective, it is just taking a sample of the voltage in time. I fail to see how a "misinterpretation" could be made since there is no "turning car wheel" to take pictures of at the wrong time. Do the harmonics alias in such a way that the wave shape is preserved?
In my mind, adding a filter to the signal will modify the shape of the original signal, getting rid of those upper harmonics. Depending on the filter design, it could add overshoot, ripple, and/or rise/fall time changes. So wouldn't the best representation of the pulse be obtained by direct sampling?